3×3方格数字排列概率 - 避免失望

{"title":"Problem Statement","description":"There is a 3×3 grid with numbers between 1 and 9, inclusive, written in each square. The square at the i-th row from the top and j-th column from the left (1≤i≤3,1≤j≤3) contains the number c i,j . \n\nThe same number may be written in different squares, but not in three consecutive cells vertically, horizontally, or diagonally. More precisely, it is guaranteed that c i,j satisfies all of the following conditions.\n\nc i,1 =c i,2 =c i,3 does not hold for any 1≤i≤3.\nc 1,j =c 2,j =c 3,j does not hold for any 1≤j≤3.\nc 1,1 =c 2,2 =c 3,3 does not hold.\nc 3,1 =c 2,2 =c 1,3 does not hold.\nTakahashi will see the numbers written in each cell in random order. He will get disappointed when there is a line (vertical, horizontal, or diagonal) that satisfies the following condition.\n\nThe first two squares he sees contain the same number, but the last square contains a different number.\nFind the probability that Takahashi sees the numbers in all the squares without getting disappointed.\n\nConstraints\nc i,j ∈{1,2,3,4,5,6,7,8,9} (1≤i≤3,1≤j≤3)\nFor any 1≤i≤3, c i,1 =c i,2 =c i,3 does not hold.\nFor any 1≤j≤3, c 1,j =c 2,j =c 3,j does not hold.\nc 1,1 =c 2,2 =c 3,3 does not hold.\nc 3,1 =c 2,2 =c 1,3 does not hold.","keywords":"3×3 grid, number arrangement, probability, disappointment, algorithm, constraints"}